Entropy catastrophe and superheating of crystals

Abstract

Kauzmann¹ has pointed out that at a temperature (T_k) far below the melting temperature (T_m) of a crystal, the entropies of an undercooled liquid and its corresponding equilibrium crystal tend to become equal. At temperatures below T_k, the crystal would have a greater entropy than its liquid. Such a catastrophe is avoided through a glass transition of the liquid above T_k. Fecht and Johnson² have shown that such a transition should occur for aluminium at 0.23 T_m. A similar entropy catastrophe can also arise at a temperature, T_i^S, above T_m. Above T_i^S, the crystalline solid is once again expected to have an entropy greater than that of the liquid. Cahn³ has considered the implications of this idea with respect to the superheating of a solid. Here we present an alternative evaluation of the two temperatures of instability, T_k and T_i^S, from experimentally measurable parameters. Results for alkali metals show that the Kauzmann-type entropy catastrophe occurs at about half the absolute melting temperature, whereas we find that the entropy catastrophe as described by Fecht and Johnson² occurs at twice the absolute melting temperature. For most solids, vaporization will probably intervene before the entropy catastrophe temperature above the melting temperature is reached.